In order to compare results of different Dark Matter (DM) direct
detection experiments one needs a theoretical framework in which to
interpret the data. Since the typical momentum exchanges between DM
and nuclei are small, \(q_{\rm max}\lesssim 200\)  MeV, the interactions
are well described within Effective Field Theory (EFT) without
recourse to detailed particle physics models [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}. The
interactions are ordered according to the dimensionality of the
operators, giving an effective interaction Lagrangian
\({\cal L}_\chi =\sum _{a,d}\hat{_{a}^{(d)} {\cal Q}_a^{(d)}\,,\qquad {\rm where}\quad \hat{_{a}^{(d)}=\frac{{a}^{(d)}}{\Lambda ^{d-4}}\,.}Here, a^{(d)} are dimensionless Wilson coefficients, \Lambda  isthe NP scale, generically of the order of the mediator mass, and the sum runs over the operator labels, a,and the mass dimension of the operators, d. The EFT description isvalid as long as the mediators are heavier than the momenta exchanges,q_{\rm max}\ll \Lambda .}The UV theories of DM interactions with the SM generically give anonzero contribution to at least one of the operators with d\le 7. This set of operators already covers, for instance, all thedifferent chiral structures one can form out of two DM and two SMfermion fields. Since the operators with low mass dimensions typicallygive the dominant contributions to the scattering rates, it sufficesfor most purposes to truncate the sum in (\ref {eq:lightDM:Lnf5}) atd=7. Indeed, the commonly used DM EFTs include operators up to massdimension seven~\cite {Goodman:2010qn, Bishara:2017nnn}. However, thesets used in the literature are not complete -- they do not containthe full basis of independent dimension-seven operators. In thepresent manuscript we rectify this situation.\) 
